How can I disable and lockdown the PDF File Attachments option?

As an Enterprise customer, I sometimes need to adjust our installs of Acrobat or Acrobat Reader after deployment. I want to make sure that the end users cannot change this security option, so I need an option to grey out the menu item.
Changing the setting manually via the User Interface (Preferences > Trust Manager) is not an option.

Environment

Acrobat

Acrobat Reader

Steps

Create new DWORD bAllowOpenFile in HKCU\Software\Adobe\<product: Acrobat or Reader>\<version>\Originals

Set the key to 0 to deselect option

Create new DWORD bSecureOpenFile in HKCU\Software\Adobe\<product: Acrobat or Reader>\<version>\Originals

Set the key to 1 to lockdown the option

Setting both keys will result in the option being deselected and greyed out in the UI:

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